For PRO licenses, the tire specifications now include radial stiffness.

Using the profile and radial stiffness, MotoSPEC v5.7 can calculate the 'loaded radius' of the tire with lean angle, improving the accuracy of the geometry calculations.

Using the profile and radial stiffness, MotoSPEC v5.7 can calculate the 'loaded radius' of the tire with lean angle, improving the accuracy of the geometry calculations.

The Standard license of MotoSPEC continues to use the tire center radius at zero lean angle.

MotoSPEC v5.7 now has separate forms for Front and Rear tires, and tire size and rim width can now be recorded in the tire forms.

MotoSPEC v5.7 now has separate forms for Front and Rear tires, and tire size and rim width can now be recorded in the tire forms.

__Radial Compression of the Tire__

Starting with MotoSPEC v5.5, it has been possible for PRO licenses to specify lean angle and tire profiles, which are applied in geometry calculations. This tire profile has been considered inflexible and rigidly fixed to the wheel.

Compression of the tire can be significant and alter the geometry of the motorcycle, as shown in the image below.

MotoSPEC v5.7 builds on the rigid profile specification, allowing radial stiffness to be specified. This allows the tire profile to move with respect to the rim, and allows tire compression to be calculated to further improve the accuracy of the motorcycle geometry calculations.

Image courtesy of FS-3 Racing

__Tire Model__

To account for tire compression, the tire can be simplified and modeled as the rigid tire profile supported by a radial spring to the wheel. The rate of the radial spring is equivalent to the radial stiffness of the tire.

The radial force indicated by the green arrow is the wheel force in the plane of the motorcycle, as calculated by MotoSPEC.

Lateral movement of the profile is not considered.

The radial compression of the tire profile is calculated as:

*Radial compression (mm) = Radial force (N) / Radial Stiffness (N/mm)*

The MotoSPEC tire model will be further developed and refined going forward as required.

The effects of speed and load on the stiffness are not currently considered in the tire model. Growth due to speed is also not currently considered.

If desired, it is possible to create individual tire specifications for a given tire at different speeds. For example, separate tire specifications for a single tire at 150 kph and 250 kph.

__Tire Specification with Radial Stiffness__

The Radial Stiffness Specification can be shown or hidden with the checkbox at the top left of the Tire form.

The radius stiffness for each tire can be turned on or off by checking or unchecking the 'Radial Stiffness Enabled' checkbox. This allows easy comparison of the effects of radial stiffness. The radial stiffness textboxes are greyed out when the stiffness is disabled, as seen in the form image above.

Since the radial stiffness can vary with lean angle, it is specified with pairs of lean angle and stiffness values.

MotoSPEC will linearly interpolate between specified lean angles, to determine the radial stiffness at the lean angle specified in the Dynamic Readings of each column in the MotoSPEC window.

For example, using the stiffness specification shown above for 'X 120 Slick', the radial stiffness at 45 degrees will be 210 N/mm.

When the Dynamic Reading lean angle is greater than the maximum lean angle in the radial stiffness specification, the stiffness at the maximum lean angle will be used.

For example, from the stiffness specification for 'X120 Slick' above, at 60 degrees, the radial stiffness will be 210 N/mm. Similarly, for 'X 125 Slick', radial stiffness of 200 N/mm will apply at all lean angles, even though it is only specified at zero degrees lean.

The interpolation and extension of stiffness specification is described by the graph below.

Since the radial stiffness can vary with lean angle, it is specified with pairs of lean angle and stiffness values.

MotoSPEC will linearly interpolate between specified lean angles, to determine the radial stiffness at the lean angle specified in the Dynamic Readings of each column in the MotoSPEC window.

For example, using the stiffness specification shown above for 'X 120 Slick', the radial stiffness at 45 degrees will be 210 N/mm.

When the Dynamic Reading lean angle is greater than the maximum lean angle in the radial stiffness specification, the stiffness at the maximum lean angle will be used.

For example, from the stiffness specification for 'X120 Slick' above, at 60 degrees, the radial stiffness will be 210 N/mm. Similarly, for 'X 125 Slick', radial stiffness of 200 N/mm will apply at all lean angles, even though it is only specified at zero degrees lean.

The interpolation and extension of stiffness specification is described by the graph below.

__Pressure Compensation__

The radial stiffness specification also includes pressure compensation, to correct for the difference between the operating pressure and the 'reference' pressure used when measuring the radial stiffness.

Please note that the tire pressures are specified in bar, where 1 bar = 14.50 psi.

For example:

1.38 bar = 20 psi

2.50 bar = 36.3 psi

2.50 bar = 36.3 psi

Pressure compensation requires the following parameters:

- Reference Pressure (bar): the pressure that the stiffness measurements were taken at
- Operating Pressure (bar): the pressure of the tire in use
- Pressure Coefficient (N/mm / bar): a scaling factor for the effect the difference between the nominal and operating pressures.

The modified stiffness is calculated by multiplying the pressure difference (Operating P - Reference P) by the Pressure Coefficient.

*Modified stiffness = Specified stiffness +*

( Operating Pressure - Reference Pressure) x Pressure Coefficient

( Operating Pressure - Reference Pressure) x Pressure Coefficient

For example, using the tire specification above, at 30 degrees:

*Modified Stiffness = 195 N/mm + (2.30 bar - 2.50 bar) x 50 N/mm / bar = 185 N/mm*

The pressure compensation is assumed to be linear with respect to the pressure difference.

If all three parameters are not specified, the pressure compensation is not applied.

__Tire Specification Examples__

Examples of tire specifications for Dunlop superbike slicks are below.

Please note that the radial stiffness is currently only specified at zero lean.

__Comparison of Geometry with Radial Stiffness__

An example of a corner exit is shown in the image below, demonstrating one of the effects of the tire profiles, lean angle and tire stiffness.

Black = zero lean angle (using center radius, equivalent to Standard license)

Grey = lean angle

Red = lean angle + radial stiffness

Effect of tire profile and lean angle (Black vs Grey):

- The motorcycle is pitched forward approximately 0.3 degrees, as seen comparing the rake and swingarm angles.
- This is caused by the front tire radius decreasing more than the rear with lean angle, due to the difference in profiles.
- The anti-squat angle is smaller due to the reduced radius of the rear tire with lean angle.
- The trail is smaller due to the reduced rake and also the smaller radius of the front tire.

Effect of radial stiffness (Grey vs Red):

- The rake and swingarm angle are increased, due to the rear tire being less stiff than the front tire.
- The anti-squat angle is smaller due to compression of the rear tire.
- The trail is slightly increased due to the increased rake, even though the front tire radius is smaller due to the compression.

__Representation of Tire Compression in Chassis Graph__

The image below shows how bike is represented in the CHASSIS graph when the radial stiffness is enabled.